KAMPALA, Uganda — The foot soldiers searching the deep jungles on the hunt for African warlord Joseph Kony were convinced they had cornered his deputy as they exchanged gunfire with a band of Lord's Resistance Army rebels.

When the shooting subsided, the soldiers found a pair of lifeless rebels and two children deserted by insurgents.

But the deputy — Dominic Ongwen, the subject of an international arrest warrant — had escaped, leaving his pursuers to rue a missed opportunity.

The shootout in August in the Central African Republic highlighted the limitations of African efforts to eliminate the leadership of the Lord's Resistance Army (LRA), a brutal gang of jungle militiamen with no real political aim except violence and destruction.

Roughly one year after 100 U.S. Special Forces troops arrived in four Central Africa nations to advise African soldiers in their pursuit, Kony is still on the run and his exact whereabouts unknown.

Ugandan officials now say he is hiding in a place called Kafia Kingi, along the volatile Sudan-South Sudan border.

When President Obama announced in October 2011 that he was sending in the forces, American policymakers and Africa specialists warned that, even with the extra U.S. assistance, the hunt for a killer in an expansive jungle the size of France would be difficult. The warnings have proved to be true.

Despite a spike in LRA defections and statements by the State Department that significant progress has been made, those most interested in the Kony hunt are calling for even greater U.S. involvement.

A ‘challenging’ endeavor

Kasper Agger, a researcher with the U.S.-based anti-genocide group the Enough Project, said in a recent report that U.S. forces must “play a more operational role” in the hunt. American forces now don’t participate in the physical hunts and engage in combat only in cases of self-defense.

Mr. Agger said the mission to catch LRA leaders is impossible without more troops on the ground and greater investment in human and aerial intelligence.

Ugandan officials want America to provide more advanced technology that might make it possible to map LRA movements.

Military spokesman Col. Felix Kulayigye praised the U.S. for supplying helicopters and troops for helping to drive defections from the Lord's Resistance Army, but he asserted that “they need to invest more in technology.”

Isolating LRA rebels has proved difficult in a jungle teeming with cattle keepers and illegal hunters, as well as other militias that have nothing to do with the rebel group, Col. Kulayigye said.

“How do you tell that these are the LRA and these are civilians looking after their cattle? It’s a challenge,” Col. Kulayigye said.

The three, including Kony, are wanted by the International Criminal Court on charges of committing war crimes and crimes against humanity over two decades in Uganda and later in South Sudan, Congo and the Central African Republic, the four countries where U.S. forces have been deployed.

At the peak of its powers, the Lord's Resistance Army was a cruel group whose ragtag fighters razed villages, raped women and amputated limbs.

In Uganda, where the Lord's Resistance Army was born in the 1980s as a popular uprising against President Yoweri Museveni, the insurgency killed hundreds of people and sent millions fleeing into filthy camps for the internally displaced.

The Lord's Resistance Army is especially notorious for recruiting boys to fight and for taking girls as sex slaves, the reason the U.S. charity Invisible Children started a successful online video campaign early this year to raise global awareness of the rebels’ crimes.

This year alone the Lord's Resistance Army killed 39 civilians in Congo and the Central African Republic, U.N. Secretary-General Ban Ki-moon said in a report this month. An additional 193 people were abducted in both countries, Mr. Ban’s report to the U.N. Security Council said.

‘Significant progress’

The African Union this year endorsed the creation of a force to hunt down the militia’s leaders, with all LRA-affected countries expected to contribute toward the envisaged force of 5,000 soldiers.

But several months later, only about 2,500 troops, the bulk of them Ugandan and a few hundred soldiers from South Sudan and the Central African Republic, have materialized for the mission. Congo has yet to make a contribution.

The U.S. has spent $30 million every year since 2008 on the LRA mission, including on supplies such as fuel for helicopters, according to Daniel Travis, a U.S. Embassy spokesman in Uganda.

Hilary Renner, the spokeswoman for the State Department’s Africa bureau, cited the capture in May of Caesar Acellam, a top LRA strategist, as well as the near-capture of Ongwen as examples of “significant progress” made in efforts to weaken the Lord's Resistance Army.

“Defections from the LRA’s ranks have significantly increased over recent months,” Ms. Renner said. “Since Acellam’s capture, several mid-level officers have left the group.

“We are working with the regional forces and nongovernmental organizations to airdrop more leaflets, expand radio broadcasts, and establish safe reporting sites to encourage the remaining LRA to peacefully surrender from the group,” she said.

Angelo Izama, an analyst who runs a Kampala-based security think tank called Fanaka Kwawote, said the Lord's Resistance Army would be even weaker today if countries like Congo and the Central African Republic became as committed as the Ugandans are to fighting the rebels.

“The Americans could open a new front with the Central African Republic authorities and pursue Kony with more flexibility from that side,” Mr. Izama said.

It remains unclear how long the U.S. troops will stay in Africa, especially if the LRA leaders continue to remain elusive. Ms. Renner said U.S. officials continue to talk with their African partners to ensure the American presence is having its intended security effect.

Ugandan military officials insist that the Lord's Resistance Army, even if its top leaders remain free, is degraded and fading fast, with its fighters — about 200 combatants — constantly moving to avoid detection and struggling for food.

“Kony has been denied the freedom to abduct at will,” Col. Kulayigye said. “He can’t increase his numbers.”